# Game Theory Week 2 Quiz Answers

## Game Theory Week 2 Quiz Answers

In this article i am go to share Coursera Course Game Theory Week 2 Quiz Answers with you..

### Week 2 Quiz Answers

Question 1)

Find a mixed strategy Nash equilibrium where player 1 randomizes over the pure strategy Left and Right with probability pp for Left. What is pp?

• 1/2
• 2/3
• 1/4
• 3/4

Question 2)

In a mixed strategy Nash equilibrium where player 1 plays Left with probability pp and player 2 plays Left with probability qq. How do pp and qq change as XX is increased (X>1X>1)?
• p is the same, q decreases.
• p increases, q increases.
• p decreases, q decreases.
• p is the same, q increases.

Question 3)
• There are 2 firms, each advertising an available job opening.
• Firms offer different wages: Firm 1 offers w_1=4w1​=4 and 2 offers w_2=6w2​=6.
• There are two unemployed workers looking for jobs. They simultaneously apply to either of the firms.
• If only one worker applies to a firm, then he/she gets the job
• If both workers apply to the same firm, the firm hires a worker at random and the other worker remains unemployed (and receives a payoff of 0).
Find a mixed strategy Nash Equilibrium where pp is the probability that worker 1 applies to firm 1 and qq is the probability that worker 2 applies to firm 1.

• p=q=1/4p=q=1/4;
• p=q=1/2p=q=1/2;
• p=q=1/5p=q=1/5.
• p=q=1/3p=q=1/3;

Question 4)
• A king is deciding where to hide his treasure, while a pirate is deciding where to look for the treasure.
• The payoff to the king from successfully hiding the treasure is 5 and from having it found is 2.
• The payoff to the pirate from finding the treasure is 9 and from not finding it is 4.
• The king can hide it in location X, Y or Z.

Suppose the pirate has two pure strategies: inspect both X and Y (they are close together), or just inspect Z (it is far away). Find a mixed strategy Nash equilibrium where pp is the probability the treasure is hidden in X or Y and 1-p1−p that it is hidden in Z (treat the king as having two strategies) and qq is the probability that the pirate inspects X and Y:

• p=4/9p=4/9, q=2/5q=2/5;
• p=1/2p=1/2, q=1/2q=1/2;
• p=5/9p=5/9, q=3/5q=3/5;
• p=2/5p=2/5, q=4/9q=4/9;

Question 5)
• A king is deciding where to hide his treasure, while a pirate is deciding where to look for the treasure.
• The payoff to the king from successfully hiding the treasure is 5 and from having it found is 2.
• The payoff to the pirate from finding the treasure is 9 and from not finding it is 4.
• The king can hide it in location X, Y or Z.

Suppose that the pirate can investigate any two locations, so has three pure strategies: inspect XY or YZ or XZ. Find a mixed strategy Nash equilibrium where the king mixes over three locations (X, Y, Z) and the pirate mixes over (XY, YZ, XZ). The following probabilities (king), (pirate) form an equilibrium:

• (1/3, 1/3, 1/3), (4/9, 4/9, 1/9);
• (1/3, 1/3, 1/3), (1/3, 1/3, 1/3);
• (4/9, 4/9, 1/9), (1/3, 1/3, 1/3);
• (1/3, 1/3, 1/3), (2/5, 2/5, 1/5);